Download Fundamental problems of algorithmic algebra (draft) by Chee-Keng Yap PDF

By Chee-Keng Yap

Show description

Read Online or Download Fundamental problems of algorithmic algebra (draft) PDF

Similar algebra books

Groebner bases algorithm: an introduction

Groebner Bases is a method that gives algorithmic ideas to quite a few difficulties in Commutative Algebra and Algebraic Geometry. during this introductory educational the fundamental algorithms in addition to their generalization for computing Groebner foundation of a suite of multivariate polynomials are provided.

The Racah-Wigner algebra in quantum theory

The improvement of the algebraic facets of angular momentum concept and the connection among angular momentum conception and designated themes in physics and arithmetic are lined during this quantity.

Wirtschaftsmathematik für Studium und Praxis 1: Lineare Algebra

Die "Wirtschaftsmathematik" ist eine Zusammenfassung der in den Wirtschaftswissenschaften gemeinhin benötigten mathematischen Kenntnisse. Lineare Algebra führt in die Vektor- und Matrizenrechnung ein, stellt Lineare Gleichungssysteme vor, berichtet über Determinanten und liefert Grundlagen der Eigenwerttheorie und Aussagen zur Definitheit von Matrizen.

Extra resources for Fundamental problems of algorithmic algebra (draft)

Example text

S. Householder. Principles of Numerical Analysis. McGraw-Hill, New York, 1953. [86] L. K. Hua. Introduction to Number Theory. Springer-Verlag, Berlin, 1982. ¨ [87] A. Hurwitz. Uber die Tr¨ agheitsformem eines algebraischen Moduls. Ann. Mat. , 3(20):113–151, 1913. [88] D. T. Huynh. A superexponential lower bound for Gr¨ obner bases and Church-Rosser commutative Thue systems. Info. and Computation, 68:196–206, 1986. [89] C. S. Iliopoulous. Worst-case complexity bounds on algorithms for computing the canonical structure of finite Abelian groups and Hermite and Smith normal form of an integer matrix.

217] C. K. Yap. A new lower bound construction for commutative Thue systems with applications. J. of Symbolic Computation, 12:1–28, 1991. [218] C. K. Yap. Fast unimodular reductions: planar integer lattices. IEEE Foundations of Computer Science, 33:437–446, 1992. [219] C. K. Yap. A double exponential lower bound for degree-compatible Gr¨ obner bases. Technical Report B-88-07, Fachbereich Mathematik, Institut f¨ ur Informatik, Freie Universit¨ at Berlin, October 1988. [220] K. Yokoyama, M. Noro, and T.

Then m, n ∈ Z has the property that m | n iff (m) ⊇ (n), “agreeing” with our definition. In general, the relationship between ideal quotient and divisor property is only uni-directional: for ideals I, J ⊆ D, we have that I ⊇ IJ and so I divides IJ. The GCD of a set S of ideals is by definition the smallest ideal that divides each I ∈ S, and we easily verify that GCD(S) = I. I∈S For I = (a1 , . . , am ) and J = (b1 , . . , bn ), we have GCD(I, J) = I + J = (a1 , . . , am , b1 , . . , bn ). (1) So the GCD problem for ideals is trivial unless we require some other conditions on the ideal generators.

Download PDF sample

Rated 4.40 of 5 – based on 26 votes